Use the following steps to add a Public IP address to an Azure VM which is already created and running or stopped.
1. Go to the Virtual machine and click on Networking under VM Settings in Virtual Machine blade.
2. Click on the Network Interface of the Virtual Machine.
3. Click on the IP Configuration under settings in the Network Interface blade.
4. Click on the IP Configuration of the Virtual machine.
5. Click Enabled under Public IP Address Settings and then click on Configure Additional Settings.
6. Click on Create New on Choose Public IP address blade.
7. Give the Public IP Address a name, select static and click OK.
8. Click Save on IP configuration blade.
9. Wait for the IP to be created and network interface to save. Close the IP Config blade, close the network interface blade, Close the network blade.
10. Click on your Virtual machine and you will have a Public IP listed under Public IP Address on the Virtual machine Overview.